If your HomePod mini is connected to the power supply means that it’s ready to use. To turn your HomePod off, you have to simply switch the power off or unplug the power cable from the socket. You have to know that the HomePod mini can’t be turned off by any command or button.
When you’re ready to turn your HomePod back on, and you don’t know how to do so visit this article:
Remember that you don’t have to turn off your speaker when is not in use. If you don’t want to use your speaker at the moment, for example, your HomePod is playing some music and you want to stop it simply say: “Hey Siri Stop” and the music stops.